Because we are on an alternate history site, and because we are discussing the fate of carriers in a nuclear exchange, any thoughts on a change in balance of naval power of the Soviet R-27K asbm came into service? I have to imagine the threat of a nigh-uninterceptable high-precision nuclear missile specifically designed to target ships would force the US to re-think their naval strategy in some way. (The R-27K was taken out of service due to SALT)
It's the targetting that's the trick.
It goes something like this: a CVBG has a carrier, two guided missile cruisers for area air defence, maybe an UNREP ship, and a handful of DDGs (or maybe FFs, though they are slow and the USN would rather put them with convoys or the Marines). They're in a sort of blob centred on the carrier, with the cruisers within couple of miles, maybe a FF as a goalkeeper and plane guard, and then the DDs in a ring up to 10 miles out from the carrier as they put on a burst of speed and then slow down to maintaining steerage to give their sonars the best chance to hear stuff without making much noise.
Around the formation are helicopters with dipping sonars making sure the DDs don't miss anything.
Out another dozen miles at least (sprinting and drifting like the DDs) is an SSN, going where the carrier goes along its axis of advance, because it's a lot quieter than those ASW DDs and can hear better.
Off-axis a bit and maybe 50 miles out an E-2 does a slow oval keeping an eye on air and ocean for about 200 miles in every direction. There's another one on the other side of the carrier, just in case anybody on the Red team is getting sneaky.
Loafing around drinking coffee is an S-3 waiting for somebody on the surface to hear a submarine, at which point it will zoom over to the contact and try to localize it with sonobuoys and then kill it with lightweight torpedoes. and possibly if the tensions are high there's also an EA-6 (whose crew are drinking coffee that tastes even better because of the gold in the canopy).
About 80-100 miles from the carrier in the vague direction of the E-2 closer to the expected threat direction (i.e. towards the Kola Peninsula, if we're in the North Atlantic) are a couple of pairs of Tomcats with four Phoenixes and a pair each Sparrows and Sidewinders.
The Soviet challenge is to get a big fat lumbering 550kt turboprop (giant radar-cross-section from those propellers) Bear maritime patrol aircraft within 200 nm of the carrier at a high enough altitude that it's got line of sight, then to switch on the surface search radar (which, electronically speaking, is like jumping up and down and screaming "HEY GUYS, LOOK AT ME, I'M OVER HERE!"), not get fooled by decoys, chaff, jamming, spoofing or the other ships in close company with the carrier, and then pass on the contact information to the loitering regiments of Soviet Naval Aviation bombers when contested by the EW of an EA-6 Prowler, before that Bear is itself found by a Mach 5 active radar-homing AAM.
The E-2s are trying to find the Tu-95 and tell the F-14s where it is in time for them to kill it (and they will - the AIM-54 Phoenix is really designed specifically to do this one job) before the Tu-95 can find the carrier and tell the lurking SSGNs (and SSGs
Golf for the R-27K) and loitering Soviet Naval Aviation bomber regiments where it is.
The USN plan has the Tu-95 getting splashed 50-100nm short of detection range of the carrier. The SNA plan has the F-14s having to lob their AIM-54s at incoming Kh-22 missiles headed for the carrier group, at which point the bombers and MPA run away.
At the start of the war, the Tu-95 can get within radar range of the carrier group without being shot, but the bomber regiments can't, because flying a regiment of Backfires over Finland and Norway to hunt a
Nimitz-class is a dead giveaway that the balloon is going to go up in the next few hours, and the Shock Armies and Frontal Aviation will be rather cross if their surprise is spoiled like that. So the opening shots have got to solely be from SSGNs not-very-near the carrier (because big fat slow SSGNs which are also very near the carrier get found and sunk by the 688 class, S-3s, or SH-60Fs with the carrier).
Equally, there's a pretty decent chance that the SSGNs have picked up a completely separate trailer NATO SSN if they cross the SOSUS line, sitting within torpedo range and trying quite hard not to be heard. Cue lots of clichés from
Red Storm Rising about playing Cowboys and Cossacks. But as was pointed out upthread, there just aren't that many SSGNs and there are quite a few 688s and
Trafalgars whose day job is to hunt them down. If a
Charlie or
Golf starts launching missiles, depending on the ROE at the time, it may not survive to flush all its tubes.
But there's a much better chance of at least some of the Soviet pieces being in place at the start of the war, than after it goes hot and the USN is free to engage anything flying near a CVBG to make extra sure that nobody gets targetting data on the carrier.